Putting to one side questions of protecting against physical tampering (e.g. of the underlying database), since you've stipulated that physical security is not the present concern...
I think the primary consideration is how to ensure that a given voter votes only once. At a paper poll, each registered voter is restricted to a particular booth/location and verification is done by name+SSN and a signature.
You might need a high resolution digital signature capture and therefore a touchscreen capture peripheral or a touch screen terminal. A more sophisticated approach would be a biometric scanner, but that would require government records of thumb/finger prints or retinal scan - I can already see the privacy advocates lining up at the lawyer's offices.
Another approach would be for the voter "registrar office" to issue digital keys to each voter prior to the election - a (relatively) short (cryptographically strong) random alpha/numeric key that is entered with the voter's name and/or SSN into the application. Knowledge of that key is required for that particular voter in that particular election. These keys would be issued by post in tamper-evident envelopes, like those used by banks for postal confirmation of wire transfers and delivery of PIN numbers. The key must include checksum data so that the user can have the entry of it immediately validated and it should be in groups of 4, so something like XXXX-XXXX-XXXX-CCCC.
Any other "secret" knowledge, such as SSN, is likely too easily discovered for a large percentage of the population (though we don't seem to be able to make credit-granting organizations understand this), and therefore is unsuitable for authentication.
Vote counting can be done by generating a public key encrypted data file which is transferred (by sneaker net?) to the central system. This must include the "voting booth" identity information and a record for each voter including their SSN and the digital key (or signature, or biometric data). Votes with invalid keys are eliminated. Multiple votes with the same key and same votes are treated as a single vote for that candidate. Multiple votes with the same key and different votes are flagged for fraud investigation (with the constituent contacted by phone, issued a new key, and directed to revote).